Several models of nonlinear oscillators within the framework of a tomographic probability representation of quantum mechanics are discussed. The tomograms of the states satisfying the time dependent Schrödinger equation with the nonlinear Hamiltonians are obtained. The case of the quadratic Hamiltonian of the general form is considered in detail. Using the knowledge about the Green's function of such systems the time dependent tomogram is deduced and several examples of the quadratic Hamiltonian systems are studied in details. Next, the quasi-quadratic Hamiltonian systems are considered. In particular, the method given in [1,2] to introduce the tomogram for states whose Wigner function is a delta function is used. The cases of the coherent and the Fock bases defining the states are considered and the tomograms corresponding to these cases are studied.